High speed contouring enhanced with C2 PH quintic spline curves

This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a “good” interpolant to the nodal points of the cubic B-spline curve, with the same knot vector and control points. To generate the C2 PH quintic spline curves, a uniform knot sequence is employed. The S-curve motion planning architecture, with variable feedrate for a planar C2 PH quintic spline curve, is also developed. In particular, C1 cubic feed acceleration/deceleration is imposed on the first and last PH quintic spline segments. Several closed C2 PH quintic spline curve contouring tasks, along with a simple position loop controller, were conducted to verify the effectiveness of the proposed interpolation algorithm. The experimental results were analyzed and discussed. It is found that the proposed CNC interpolator is not only feasible for machining the complicated parametric curves represented in the C2 PH quintic spline form, but also yields a satisfactory contouring performance for variable feedrate control.